Fractions Equal Parts

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Answer Key & Explanations

Fractions Equal Parts · Grade 3 · Worksheet 2

1. Liam is helping his teacher organize the classroom library. They have 72 books that need to be placed equally on 8 shelves. How many books should Liam put on each shelf? Answer: 9 Solution: We have 72 books total and 8 shelves. We want to split the books equally among the shelves. That means we need to divide 72 by 8.
   Full step-by-step solution

   We have 72 books total and 8 shelves. We want to split the books equally among the shelves. That means we need to divide 72 by 8. Step 1: Write the division problem. 72 ÷ 8 = ? Step 2: Think about multiplication — what number times 8 equals 72? 8 × 9 = 72. Step 3: So, 72 ÷ 8 = 9. Step 4: This means each shelf gets 9 books. Answer: Liam should put 9 books on each shelf.

2. Shade 9/10 of the rectangle. Answer: 9/10 Solution: The rectangle is divided into 10 equal parts. This means the denominator of the fraction is 10. We need to shade 9/10 of the rectangle.
   Full step-by-step solution

   Step 1: The rectangle is divided into 10 equal parts. This means the denominator of the fraction is 10. Step 2: We need to shade 9/10 of the rectangle. The numerator 9 tells us how many parts to shade. Step 3: Count out 9 of the 10 equal parts and shade them. Step 4: The shaded part represents 9 out of 10, or 9/10. The answer is 9/10.

3. Liam baked a large rectangular cake for his class party. He cut the cake into 8 equal slices. If 5 students each take one slice, what fraction of the whole cake did they take? Answer: 5/8 Solution: Liam cut the cake into 8 equal slices. This means the whole cake is represented as 8/8. Determine how many slices were taken.
   Full step-by-step solution

   Step 1: Understand the cake cutting. Liam cut the cake into 8 equal slices. This means the whole cake is represented as 8/8. Step 2: Determine how many slices were taken. 5 students each take 1 slice, so 5 slices are taken. Step 3: Write the fraction of the cake taken. Since each slice is 1/8 of the cake, 5 slices represent 5 × (1/8) = 5/8 of the cake. Step 4: Interpret the result. The fraction 5/8 means 5 out of 8 equal parts of the cake were taken by the students. Final Answer: 5/8

4. Matiu shades 5/8 of a rectangle divided into equal parts. What fraction of the rectangle is NOT shaded? Answer: 3/8 Solution: The rectangle is divided into 8 equal parts. This means the whole is 8/8. Matiu shades 5 of the 8 parts, which is the fraction 5/8.
   Full step-by-step solution

   Step 1: The rectangle is divided into 8 equal parts. This means the whole is 8/8. Step 2: Matiu shades 5 of the 8 parts, which is the fraction 5/8. Step 3: To find the fraction not shaded, subtract the shaded part from the whole: 8/8 - 5/8 = 3/8. Step 4: So, 3/8 of the rectangle is not shaded. The answer is 3/8.

5. Emma is helping her teacher organize the classroom art supplies. They have a large rectangular sheet of colored paper that is 84 inches long. Emma needs to cut it into 7 equal strips for a class project. How many inches long will each strip be? Answer: 12 Solution: The total length of the paper is 84 inches. Emma needs to cut it into 7 equal strips.
   Full step-by-step solution

   Step 1: The total length of the paper is 84 inches. Step 2: Emma needs to cut it into 7 equal strips. Step 3: To find the length of each strip, divide the total length by the number of strips: 84 ÷ 7 Step 4: 84 ÷ 7 = 12 Each strip will be 12 inches long.

6. Shade 9/11 of the rectangle. Answer: 9/11 Solution: The rectangle is divided into 11 equal parts. The denominator is 11, which tells us the total number of equal parts. Step 2: The numerator is 9, which tells us how many parts to shade.
   Full step-by-step solution

   Step 1: The rectangle is divided into 11 equal parts. The denominator is 11, which tells us the total number of equal parts. Step 2: The numerator is 9, which tells us how many parts to shade. Step 3: Shade 9 of the 11 equal parts. Step 4: The shaded fraction is 9/11. The answer is 9/11.

7. A rectangular garden is divided into 16 equal square plots. The gardener plants flowers in 5 plots and vegetables in 7 plots. The remaining plots are left empty. What fraction of the garden is planted with crops? Answer: 3/4 Solution: Find the total number of plots planted with crops. Flowers: 5 plots Vegetables: 7 plots Total planted plots = 5 + 7 = 12 plots The garden has 16 equal plots total. Write the fraction of planted plots.
   Full step-by-step solution

   Step 1: Find the total number of plots planted with crops. Flowers: 5 plots Vegetables: 7 plots Total planted plots = 5 + 7 = 12 plots Step 2: The garden has 16 equal plots total. Step 3: Write the fraction of planted plots. Fraction = (planted plots) / (total plots) = 12/16 Step 4: Simplify the fraction. 12/16 = (12 ÷ 4)/(16 ÷ 4) = 3/4 The answer is 3/4.

8. Emma is helping her teacher organize the classroom art supplies. They have 84 crayons that need to be sorted equally into 6 boxes. How many crayons should Emma put in each box? Answer: 14 Solution: Emma has 84 crayons total She needs to divide them equally into 6 boxes To find how many crayons go in each box, divide 84 by 6 84 ÷ 6 = 14 Check: 14 crayons × 6 boxes = 84 crayons total Emma should put 14 crayons in each box.
   Full step-by-step solution

   Step 1: Emma has 84 crayons total Step 2: She needs to divide them equally into 6 boxes Step 3: To find how many crayons go in each box, divide 84 by 6 Step 4: 84 ÷ 6 = 14 Step 5: Check: 14 crayons × 6 boxes = 84 crayons total Emma should put 14 crayons in each box.

9. A rectangular garden is divided into 8 equal sections. 3 sections are planted with carrots and 2 sections are planted with tomatoes. What fraction of the garden is planted with vegetables? Answer: 5/8 Solution: The garden is divided into 8 equal sections. Carrots take 3 sections, tomatoes take 2 sections. We want the fraction of the garden planted with vegetables.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. Carrots take 3 sections, tomatoes take 2 sections. We want the fraction of the garden planted with vegetables. Step 2: Find the total number of sections with vegetables. Sections with carrots = 3 Sections with tomatoes = 2 Total vegetable sections = 3 + 2 = 5 Step 3: Write the fraction of the garden that is vegetables. The garden has 8 equal sections in total, so the fraction is: (Total vegetable sections) / (Total sections) = 5 / 8 Step 4: Conclusion. The fraction of the garden planted with vegetables is 5/8.